Question: Gabriela is 12 years older than Tiffany. Eight years ago, Gabriela was 5 times as old as Tiffany. How old is Gabriela now?
Explanation: We can use the given information to write down two equations that describe the ages of Gabriela and Tiffany. Let Gabriela's current age be $g$ and Tiffany's current age be $t$ The information in the first sentence can be expressed in the following equation: $g = t + 12$ Eight years ago, Gabriela was $g - 8$ years old, and Tiffany was $t - 8$ years old. The information in the second sentence can be expressed in the following equation: $g - 8 = 5(t - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $t$ and substitute it into our second equation. Solving our first equation for $t$ , we get: $t = g - 12$ . Substituting this into our second equation, we get the equation: $g - 8 = 5($ $(g - 12)$ $ -$ $ 8)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 8 = 5g - 100$ Solving for $g$ , we get: $4 g = 92$ $g = 23$.